Biomass partitioning and gas exchange parameters in different Musa cultivars as influenced by natural shade

Poster presented at Tropentag 2011 Development on the Margin. Bonn (Germany), 3-7 Oct 2011

Photosynthesis of three dessert banana cultivars along an altitudinal gradient

Poster presented at Tropentag 2011 - Development on the Margin. Bonn (Germany), 3-7 Oct 2011

The response of Musa cultivar root systems to a tree shade gradient

Poster presented at Tropentag 2011 - Development on the Margin. Bonn (Germany), 3-7 Oct 2011

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Slower recovery in space before collapse of connected populations

Slower recovery from perturbations near a tipping point and its indirect signatures in fluctuation patterns have been suggested to foreshadow catastrophes in a wide variety of systems. Recent studies of populations in the field and in the laboratory have used time-series data to confirm some of the theoretically predicted early warning indicators, such as an increase in recovery time or in the size and timescale of fluctuations. However, the predictive power of temporal warning signals is limited by the demand for long-term observations. Large-scale spatial data are more accessible, but the performance of warning signals in spatially extended systems needs to be examined empirically. Here we use spatially extended yeast populations, an experimental system with a fold bifurcation (tipping point), to evaluate early warning signals based on spatio-temporal fluctuations and to identify a novel spatial warning indicator. We found that two leading indicators based on fluctuations increased before collapse of connected populations; however, the magnitudes of the increases were smaller than those observed in isolated populations, possibly because local variation is reduced by dispersal. Furthermore, we propose a generic indicator based on deterministic spatial patterns, which we call ‘recovery length’. As the spatial counterpart of recovery time, recovery length is the distance necessary for connected populations to recover from spatial perturbations. In our experiments, recovery length increased substantially before population collapse, suggesting that the spatial scale of recovery can provide a superior warning signal before tipping points in spatially extended systems.United States. National Institutes of Health (NIH R00 GM085279-02)United States. National Institutes of Health (NIH DP2)Alfred P. Sloan FoundationNational Science Foundation (U.S.

Green and animal manure use in organic field crop systems

Dual-use cover/green manure (CGM) crops and animal manure are used to supply nitrogen (N) and phosphorus (P) to organically grown field crops. A comprehensive review of previous research was conducted to identify how CGM crops and animal manure have been used to meet N and P needs of organic field crops, and to identify knowledge gaps to direct future research efforts. Results indicate that: (a) CGM crops are used to provide N to subsequent cash crops in rotations; (b) CGM-supplied N generally can meet field crop needs in warm, humid regions but is insufficient for organic grain crops grown in cool and sub-humid regions; (c) adoption of conservation tillage practices can create or exacerbate N deficiencies; (d) excess N and P can result where animal manures are accessible if application rates are not carefully managed; and (e) integrating animal grazing into organic field crop systems has potential benefits but is generally not practiced. Work is needed to better understand the mechanisms governing the release of N by CGM crops to subsequent cash crops, and the legacy effects of animal manure applications in cool and sub-humid regions. The benefits and synergies that can occur by combining targeted animal grazing and CGMs on soil N, P, and other nutrients should be investigated. Improved communication and networking among researchers can aid efforts to solve soil fertility challenges faced by organic farmers when growing field crops in North America and elsewhere

The Effect of Carbon Credits on Savanna Land Management and Priorities for Biodiversity Conservation

Carbon finance offers the potential to change land management and conservation planning priorities. We develop a novel approach to planning for improved land management to conserve biodiversity while utilizing potential revenue from carbon biosequestration. We apply our approach in northern Australia's tropical savanna, a region of global significance for biodiversity and carbon storage, both of which are threatened by current fire and grazing regimes. Our approach aims to identify priority locations for protecting species and vegetation communities by retaining existing vegetation and managing fire and grazing regimes at a minimum cost. We explore the impact of accounting for potential carbon revenue (using a carbon price of US$14 per tonne of carbon dioxide equivalent) on priority areas for conservation and the impact of explicitly protecting carbon stocks in addition to biodiversity. Our results show that improved management can potentially raise approximately US$5 per hectare per year in carbon revenue and prevent the release of 1–2 billion tonnes of carbon dioxide equivalent over approximately 90 years. This revenue could be used to reduce the costs of improved land management by three quarters or double the number of biodiversity targets achieved and meet carbon storage targets for the same cost. These results are based on generalised cost and carbon data; more comprehensive applications will rely on fine scale, site-specific data and a supportive policy environment. Our research illustrates that the duel objective of conserving biodiversity and reducing the release of greenhouse gases offers important opportunities for cost-effective land management investments